Floating memristor emulator

ABSTRACT

The floating memristor emulator is based on a circuit implementation that uses grounded capacitors and CFOAs in addition to combinations of diodes and resistors to provide the required nonlinearity and time constants. This circuit results in low power consumption, cost reduction and ease of implementation because it avoids the use of multipliers, ADCs and RDACs. The present circuit is used in an FM demodulator, which exploits the frequency-dependence of the memristance. Successful use in the FM demodulator confirmed the functionality of the present floating memristor emulator circuit.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to memristors, and particularly to a floating memristor emulator that can be used in frequency-to-voltage conversion.

2. Description of the Related Art

Since its inception, several emulators have been presented for the grounded memristor. However, only few floating memristor emulators are available in the literature. Those few designs have numerous components, which present size and power consumption problems.

Thus, a floating memristor emulator solving the aforementioned problems is desired.

SUMMARY OF THE INVENTION

The floating memristor emulator is based on a circuit implementation that uses grounded capacitors and CFOAs in addition to combinations of diodes and resistors to provide the required nonlinearity and time constants. This circuit results in low power consumption, cost reduction and ease of implementation because it avoids the use of multipliers, ADCs and RDACs. The present circuit may be used in an FM demodulator, which exploits the frequency-dependence of the memristance. Successful use in the FM demodulator confirmed the functionality of the present floating memristor emulator circuit.

These and other features of the present invention will become readily apparent upon further review of the following specification and drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram of a floating memristor emulator according to the present invention.

FIG. 2A is a schematic diagram showing an I_(M) model in terms of input current for a floating memristor emulator according to the present invention.

FIG. 2B is a schematic diagram showing an I_(R) model in terms of emulator current for a floating memristor emulator according to the present invention.

FIG. 3A is a plot showing current and voltage waveform characteristics of the floating memristor emulator according to the present invention.

FIG. 3B is a plot showing current-voltage characteristics with a wide difference in the resistance values of the floating memristor emulator according to the present invention.

FIG. 4A is a plot showing current and voltage waveform characteristics of the floating memristor emulator according to the present invention at 2.9 kHz.

FIG. 4B is a plot showing current-voltage characteristics with narrow difference in resistance values at 2.9 kHz of the floating memristor emulator according to the present invention.

FIG. 5 is a plot showing behavior at 6.0 kHz of the floating memristor emulator according to the present invention.

FIG. 6 is a schematic diagram showing a test circuit for the floating memristor emulator according to the present invention.

FIG. 7 is a schematic diagram showing a FM demodulator using the floating memristor emulator according to the present invention.

FIG. 8 is a plot showing FM and the converted AM of the FM demodulator using the floating memristor emulator according to the present invention.

FIG. 9 is a plot showing the converted AM signal and the output demodulated signal of the FM demodulator using the floating memristor emulator according to the present invention.

FIG. 10 is a plot showing the input FM signal and the output modulating signal at the output of the low pass filter connected to the FM demodulator using the floating memristor emulator according to the present invention.

Similar reference characters denote corresponding features consistently throughout the attached drawings.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The present floating memristor emulator circuit includes four current feedback operational amplifiers (CFOA's 102 a, 102 b, 102 c, and 102 d), configured as shown in FIG. 1. The first 102 a, second 102 c, third 102 b, and fourth 102 d current feedback operational amplifiers (CFOAs), each have y, x, z, and w terminals. The y terminal of first CFOA1 102 a is connected two the z terminal of the second CFOA2 102 c. The y terminal of the third CFOA3 102 b is connected to the z terminal of the fourth CFOA4 102 d. A differential voltage input, v_(inp), v_(inn) is formed from the y terminals of the first and third CFOAs (102 a, 102 b). The x terminals of CFOA1 102 a and CFOA3 102 b are in operable communication with each other. For example, a potentiometer R₁ may be connected between the x terminals of CFOA1 102 a and CFOA3 102 b (the wiper portion being connected to CFOA3 102 b). Grounded capacitors C₁ through C₄ are connected to their respective CFOAs (102 a, 102 c, 102 b, and 102 d). A parallel combination (R₃ and D₁) has a cathode portion of D) connected to the w terminal of COFA1 102 a. The R₃, D₁ combination is connected in series with the upper part of the potentiometer R₅ which is connected to the y terminal of CFOA4 102 d. The wiper portion of potentiometer R₅ is connected to ground. A parallel combination (R₂ and D₂) has an anode portion of D₂ connected to the w terminal of COFA3 102 b. The R₂, D₂ combination is connected in series with the lower part of the potentiometer R₅, which is connected to they terminal of CFOA2 102 c. The input voltage produces a current through the resistance R₁ given by:

i _(R) ₁ =(v _(inp) −v _(inn) /R ₁.  (1)

This current will flow outward from terminal x of CFOA1 (102 a) and inward into terminal x of CFOA3 102 b. This current will be induced in terminal z of CFOA1 (102 a), where it will be integrated by the capacitor C₁ to produce a voltage given by:

$\begin{matrix} {v_{R_{p}} = {\frac{1}{C_{1}}{\int{\frac{v_{inp} - v_{inn}}{R_{1}}{{t}.}}}}} & (2) \end{matrix}$

This voltage will be induced on terminal w of CFOA1 (102 a) and will produce an outward current from terminal w of CFOA1 (102 a), i_(Rp) through the parallel combination of R₃ and D₁ in series with the upper part of the potentiometer R₅. This current can be expressed as:

$\begin{matrix} {i_{R_{p}} = {\frac{v_{R_{p}}}{R_{5{upper}} + R_{{eq}\; 1}}.}} & (3) \end{matrix}$

In equation (3), R_(5upper) is the resistance of the upper part of the potentiometer R₅ and R_(eq1) is a nonlinear resistance that depends on the status of the diode D₁. The voltage at terminal y of the CFOA 4 (102 d) will depend on the status of the diode D₁. This voltage can be expressed as:

$\begin{matrix} {v_{1} = {\frac{v_{R_{p}}\mspace{14mu} R_{5{upper}}}{R_{5{upper}} + R_{{eq}\; 1}}.}} & (4) \end{matrix}$

The voltage v₁ will be induced on terminal x of the CFOA4 (102 d) and will be differentiated by the capacitor C₄. Thus, the outward current in the lower input terminal will be given by:

$\begin{matrix} {i_{inn} = {C_{4}{\frac{v_{1}}{t}.}}} & (5) \end{matrix}$

In a similar way the current i_(R) ₁ will be induced in the terminal z of CFOA3 (102 b) and will be integrated by the capacitor C₃ to produce a voltage given by:

$\begin{matrix} {v_{R_{n}} = {\frac{- 1}{C_{3}}{\int{\frac{v_{inp} - v_{inn}}{R_{1}}{{t}.}}}}} & (6) \end{matrix}$

In equations (2) and (6), the voltage v_(M)=v_(inp)−v_(inn) is the differential input voltage. The voltage v_(Rn) will be induced on terminal w of CFOA3 (102 b) and will produce an inward current i_(Rn) through the parallel combination of R₂ and D₂ in series with the lower part of the potentiometer R₅. This current can be expressed as:

$\begin{matrix} {i_{R_{n}} = {\frac{- v_{R_{n}}}{R_{5{lower}} + R_{{eq}\; 2}}.}} & (7) \end{matrix}$

In equation (6) R_(5lower) is the resistance of the lower part of the potentiometer R₅ and R_(eq2) is a nonlinear resistance that depends on the status of the diode D₂. The voltage at terminal y of CFOA2 (102 c) can be expressed as:

$\begin{matrix} {v_{2} = {\frac{v_{R_{n}}\mspace{14mu} R_{5{lower}}}{R_{5{lower}} + R_{{eq}\; 2}}.}} & (8) \end{matrix}$

In equation (8), R_(5lower) is the resistance of the lower part of the potentiometer R₅ and R_(eq2) is a nonlinear resistance that depends on the status of the diode. This voltage will be induced on terminal x of CFOA2 (102 c) and will be differentiated by the capacitor C₂. Thus, the inward current in the upper input terminal will be given by:

$\begin{matrix} {i_{inp} = {{- C_{2}}{\frac{v_{2}}{t}.}}} & (9) \end{matrix}$

Assuming that the diodes D₁ and D₂ are identical, C₁=C₃=C_(i), C₂=C₄=C_(d), R₂=R₃, and the potentiometer R₅ is midway with

${R_{5{upper}} = {R_{5{lower}} = {\frac{1}{2}R_{5}}}},$

then R_(eq1)=R_(eq2)=R_(eq),

${v_{R_{n}} = {{- v_{R_{p}}} = {{- \frac{1}{2}}v_{R}}}},$

i_(Rn)=i_(Rp)=i_(R) and v₂=−v₁. Combining equations (1) and (6), the voltage v_(R)=v_(Rp)−v_(Rn) can be expressed as:

$\begin{matrix} {v_{R} = {{v_{R_{p}} - v_{R_{n}}} = {\frac{2}{C_{i}R_{1}}{\int{v_{m}{{t}.}}}}}} & (10) \end{matrix}$

Using equations (2), (3), (6) and (7) the current i_(R)=i_(Rp)=i_(Rn) can be expressed as:

$\begin{matrix} {i_{R} = {\frac{1}{k_{1}}{\int{v_{m}{{t}.}}}}} & (11) \end{matrix}$

In equation (11) the parameter k₁ is given by,

$\begin{matrix} {k_{1} = {\frac{\left( {R_{5} + {2R_{eq}}} \right)C_{i}R_{1}}{2}.}} & (12) \end{matrix}$

Also combining equations (5) and (9) the input current can be expressed as:

$\begin{matrix} {i_{M} = {i_{inp} = {i_{inn} = {k_{2}{\frac{v_{R}}{t}.}}}}} & (13) \end{matrix}$

In equation (13) the parameter k₂ is given by:

$\begin{matrix} {k_{2} = {\frac{C_{d}R_{5}}{R_{5} + {2R_{eq}}}.}} & (14) \end{matrix}$

Equations (11) and (13) can be represented by models 200 a and 200 b of FIGS. 2A and 2B, respectively. Models 200 a and 200 b correspond to a voltage-controlled memristor, where the voltage exciting the memristor v_(M) is integrated in the form of a current i_(R). This current is converted via a nonlinear resistor to voltage v_(R), and the voltage is transformed by differentiation to the memristor current i_(M). As stated supra, the present memristor emulator circuit uses four CFOAs. They are of type AD844. Simple Germanium (Ge) diodes in the circuit provide the necessary nonlinear function. Four equal-valued, grounded capacitors (47 nF) complete the z and x terminal connections for memristor circuit 100. Two equal-valued resistors (3 kΩ) complete the w and y terminal connections for memristor circuit 100. The variability of the resistor connections, wherein the equal-valued 3 kΩ resistors are interconnected by a 1 kΩ potentiometer, allows for compensation for any mismatch between the capacitors (C₁, C₂, C₃, and C₄).

Experimental results of the floating memristor emulator circuit 100 are shown in plots 300 a, 300 b, 400 a, 400 b, and 500 of FIGS. 3A, 3B, 4A, 4B, and 5, respectively. Inspection of the plots clearly shows the frequency dependence of the memristance. As the frequency increases, the memristor emulator tends to behave as a normal resistor.

The functionality of the present floating memristor emulator circuit 100 of FIG. 1 was tested by using it in FM-to-AM conversion. The FM-AM conversion circuit 600 shown in FIG. 6 is a simple frequency dependent, variable-gain inverting amplifier exploiting to advantage the frequency dependence of the memristance to form an FM discriminator circuit that is used in the first stage of the FM demodulator 700 shown in FIG. 7. The FM-AM conversion circuit 600 was tested using an FM signal formed of a carrier of frequency=2 kHz, a modulating frequency=100 Hz and frequency deviation=900 Hz. As shown in FIG. 7, the output of FM-to-AM converter (discriminator) 600 circuit of FIG. 6 was applied to an envelope detector of the FM demodulator 700, which fully demodulates an FM signal input to the FM discriminator. A low pass filter follows the envelope detector. The first stage of the FM demodulator uses the floating memristor emulator 100 connected to the negative input of an operational amplifier OA1 with resistive negative feedback (R1). The positive input of OA1 is connected to ground. Operational amplifier OA1's output feeds a second stage (envelope detector) of the FM demodulator. The results obtained are shown in plots 800-1000 of FIGS. 8-10, respectively. Inspection of plots 800 through 1000 clearly shows that the present FM-to-AM converter works as expected and exploits to advantage the frequency dependence of the floating memristor emulator 100 of FIG. 1.

It is to be understood that the present invention is not limited to the embodiments described above, but encompasses any and all embodiments within the scope of the following claims. 

We claim:
 1. A floating memristor emulator, comprising: first, second, third, and fourth current feedback operational amplifiers (CFOAs), each of the CFOAs having y, x, z, and w terminals, the y terminal of the first CFOA being connected to the z terminal of the second CFOA, the y terminal of the third CFOA being connected to the z terminal of the fourth CFOA, and the x terminals of the first and third CFOAs being in operable communication with each other; grounded capacitors C₁ and C₃ connected to the respective z terminal of CFOAs one and three; grounded capacitors C₂ and C₄ connected to the respective x terminal of CFOAs two and four; a differential voltage input, v_(inp), v_(inn) formed from the y terminals of the first and third CFOAs; a potentiometer R₅ having first and second end terminals and a wiper, the first terminal being connected to the y terminal of the fourth CFOA, the second terminal being connected to the y terminal of the second CFOA, and the wiper being connected to ground; a first parallel resistor-diode combination R₃ and D₁ connected in series with the first terminal of the potentiometer R₅ and having a cathode portion of the diode D₁ connected to the w terminal of the first CFOA; and a second parallel resistor-diode combination R₂ and D₂ connected in series with the second terminal of the potentiometer R₅ and having an anode portion of the diode D₂ connected to the w terminal of the third CFOA.
 2. The floating memristor emulator according to claim 1, further comprising a potentiometer R₁ connected between the x terminals of the first and third CFOAs to define the operable communication between the x terminals, the wiper of potentiometer R₁ being connected to the third CFOA.
 3. The floating memristor emulator according to claim 2, wherein current through the potentiometer R₁ is characterized by the relation: i _(R) ₁ =(v _(inp) −v _(inn))/R ₁, where v_(inp) is an input voltage at they terminal of the first CFOA and v_(inn) is an input voltage at the y terminal of the third CFOA.
 4. The floating memristor emulator according to claim 3, wherein voltage at the w terminal of the first CFOA is characterized by the relation: $v_{R_{p}} = {\frac{1}{C_{1}}{\int{\frac{v_{inp} - v_{inn}}{R_{1}}{{t}.}}}}$
 5. The floating memristor emulator according to claim 4, wherein current at the w terminal of the first CFOA is characterized by the relation: ${i_{R_{p}} = \frac{v_{R_{p}}}{R_{5{upper}} + R_{{eq}\; 1}}},$ where R_(5upper) is the first terminal of potentiometer R₅, and R_(eq1) is a nonlinear equivalent resistance depending on the status of the diode D₁.
 6. The floating memristor emulator according to claim 5, wherein the voltage v₁ at terminal y of the fourth CFOA is characterized by the relation: $v_{1} = {\frac{v_{R_{p}}R_{5{upper}}}{R_{5{upper}} + R_{{eq}\; 1}}.}$
 7. The floating memristor emulator according to claim 6, wherein an outward current i_(inn) from the y terminal of the third CFOA is characterized by the relation: $i_{inn} = {C_{4}{\frac{v_{1}}{t}.}}$
 8. The floating memristor emulator according to claim 7, wherein a voltage v_(R) _(n) at the w terminal of the third CFOA is characterized by the relation: $v_{R_{n}} = {\frac{- 1}{C_{3}}{\int{\frac{v_{inp} - v_{inn}}{R_{1}}{{t}.}}}}$
 9. The floating memristor emulator according to claim 8, wherein current i_(R) _(n) at the w terminal of the third CFOA is characterized by the relation: ${i_{R_{n}} = \frac{- v_{R_{n}}}{R_{5{lower}} + R_{{eq}\; 2}}},$ where R_(5lower) is the second terminal of potentiometer R₅, and R_(eq2) is a nonlinear equivalent resistance depending on the status of the diode D₂.
 10. The floating memristor emulator according to claim 9, wherein the voltage v₂ at terminal y of the second CFOA is characterized by the relation: $v_{2} = {\frac{v_{R_{n}}R_{5{lower}}}{R_{5{lower}} + R_{{eq}\; 2}}.}$
 11. The floating memristor emulator according to claim 10, wherein an inward current i_(inp) on the y terminal of the first CFOA is characterized by the relation: $i_{inp} = {{- C_{2}}{\frac{v_{2}}{t}.}}$
 12. The floating memristor emulator according to claim 11, wherein: diodes D₁ and D₂ have identical value; an input capacitance C_(i) is characterized by the relation C₁=C₃; an output capacitance C_(d) is characterized by the relation C₂=C₄; the wiper of potentiometer is set midway with ${R_{5{lower}} = {R_{5{lower}} = {\frac{1}{2}R_{5}}}};$ and a differential voltage v_(R) from the w terminals of the first and third CFOAs is characterized by the relation: ${v_{R} = {{v_{R_{p}} - v_{R_{n}}} = {\frac{2}{C_{i}R_{1}}{\int{v_{M}{t}}}}}},$ where v_(M) is a differential input voltage characterized by the relation v_(inp)−v_(inn).
 13. The floating memristor emulator according to claim 12, wherein a differential current i_(R)=i_(Rp)=−i_(Rn) is characterized by the relation: ${i_{R} = {\frac{1}{k_{1}}{\int{v_{M}{t}}}}},$ where k₁ is a parameter characterized by the relation: $k_{1} = {\frac{\left( {R_{5} + {2R_{eq}}} \right)C_{i}R_{1}}{2}.}$
 14. The floating memristor emulator according to claim 13, wherein a differential input current i_(M) is characterized by the relation: ${i_{M} = {i_{inp} = {i_{inn} = {k_{2}\frac{v_{R}}{t}}}}},$ where k₂ is a parameter characterized by the relation: $k_{2} = {\frac{C_{d}R_{5}}{R_{5} + {2R_{{eq}\;}}}.}$
 15. The floating memristor emulator according to claim 14, further comprising: an inverting amplifier having an input and an output, the input being connected in a circuit with the floating memristor emulator, and wherein gain of the output varies in relation to a frequency of a signal at the input, defining an inverting amplifier-floating memristor circuit functioning as an FM discriminator.
 16. The floating memristor emulator according to claim 15, further comprising an AM envelope detector having an input and an output, the FM discriminator having an output connected to the input of an AM envelope detector, the envelope detector having an output fully demodulating an FM signal input to the FM discriminator. 